On Sat, Jun 06, 2015 at 07:18:19PM -0400, John Clark wrote: > On Sat, Jun 6, 2015 meekerdb <meeke...@verizon.net> wrote: > > > In a Newtonian world physics is deterministic > > > > Yes, but deterministic is not the same as predictable. > > > > > so there is an exact solution: > > > > That doesn't necessarily follow.
Actually, there is usually an existence theorem for differential equations showing the existence of an exact solution for given boundary conditions. It may well be that the solution cannot be expressed in closed form using our existing catalogue of transcendental functions, but our catalogue can always be added to, such that it becomes possible to express the exact solution in closed form. Indeed, before computers were invented, it was popular to enlarge the catalogue with solutions to certain strategic differential equations - think gamma function, Bessel functions etc, so as to tabulate numerical values to help solve other DEs. But now, with general availability of electronic computers, you may as well do it directly for the DE of interest. > Approximations can be made but in general > an exact solution to the 3 body problem would require an infinite (and not > just astronomical) number of numerical calculations. > Numerical approximations are a different matter. Even having a closed form exact solution will not help numerical predictions if the algorithms for computing it are numerically unstable. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
